Math Feed

Mathematics education and exploration

Don't miss new videos — get them as they're added

2 videos added this week4.2k subscribers588 topics

10 quadratic equations that separate experts from beginners

Test your math skills with these 10 expert-level quadratic questions designed to go beyond basic factoring and using the quadratic formulas. Get the file here: https://www.patreon.com/blackpenredpen/posts/10-quadratic-167816281 Proving the quadratic formula by using Euler’s formula https://youtu.be/9uAoZd60Bxg?is=-YThRBP16ZceEp6R 00:00 10 expert-level quadratic equation questions 00:31 Q1: Finding range of 'a' for specific real solutions 04:49 Q2: Proving the Quadratic Formula (Completing the Square) 07:44 Q3: Finding 'k' for a common root for two quadratic equations 11:15 Q4: Computing alpha^3 + beta^3 (Vieta's Theorem) 15:19 Q5: Solving a quartic equation using quadratic methods 20:21 Q6: Constructing a quadratic with reciprocal squared roots 26:01 Q7: Finding 'k' based on the difference of roots 30:09 Q8: Solving the composite equation f(f(x)) = x 37:19 Q9: Solving a reciprocal quartic equation 43:39 Q10: Finding a tangent line equation without calculus 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Get more math worksheets https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Quadratic Formula

Yesterday·youtube.com

I asked Google Gemini for nice equations and got this!

Google Gemini gave me this rational equation x^2+(x/(x+1))^2=3 and showed me how nicely designed this equation because it could be done with "completing the square" in a special way! 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Completing the Square Method Google Gemini

5 days ago·youtube.com

+10

2.685 is (almost) everywhere - Numberphile

Richard Elwes discusses Khinchin's constant which underlies 100% of numbers (but not every number). More about Jane Street Internships at https://jane-st.co/internships2027-Numberphile (episode sponsor). More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/jl8Fk7PPeOc We previously touched on the constant in this video from 2013: https://www.youtube.com/watch?v=VDD6FDhKCYA More Richard on Numberphile: https://www.youtube.com/playlist?list=PLt5AfwLFPxWI42WXh1jnv51jHrcjatrk8 More about Richard Elwes (who is based at the University of Leeds): https://richardelwes.co.uk/ Richard's latest book Huge Numbers Amazon (affiliate links)... UK: https://amzn.to/4bSZA8v US: https://amzn.to/4v3CIMp Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Video by Brady Haran & Pete McPartlan Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Khinchin's constant

1 week ago·youtube.com

+33

The triangle is 1/2 of a rectangle so why is the cone 1/3 of a cylinder?

We will see why the volume of a cone is 1/3 of the cylinder with the same base and height. First we will do a "water proof", then we will see how to use the disk method to compute the volume of the revolution of the solid. Great lesson for calculus 1 and AP calculus students. 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Volume of Cones and Cylinders

1 week ago·youtube.com

+50

Let's talk about 0^0^0 (as a multi-variable limit)

Let's invest the multivariable limit of x^y^z as (x, y, z) goes to (0, 0, 0). 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

multivariable limits

2 weeks ago·youtube.com

Holier Than Thou - Numberphile

Here's the original 'Holey Monster' video for full background: https://www.youtube.com/watch?v=BhSlqIe1CRQ More links & stuff in full description below ↓↓↓ This video features Richard Elwes. More info, including his books: https://richardelwes.co.uk/ More videos with Richard: https://www.youtube.com/playlist?list=PLt5AfwLFPxWI42WXh1jnv51jHrcjatrk8 Check out the Stella software we used: https://www.software3d.com/Stella.php The Monster Group (unrelated Numberphile video): https://www.youtube.com/watch?v=jsSeoGpiWsw Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Videos by Brady Haran Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Holey Monster

2 weeks ago·youtube.com

+22

How Riemann would probably integrate e^x from 0 to 1

Let's see how to evaluate the integral of e^x from 0 to 1 without using the Fundamental Theorem of Calculus (part 2), i.e. without finding an anti-derivative of e^x. We will use a limit of a Riemann sum along with a finite geometric series. Definition of e: https://youtu.be/oBlHiX6vrQY?si=B70DR4cVMoBaGNJb 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Riemann sums in calculus Integral of e^x

3 weeks ago·youtube.com

+14

Cutting Moons (Dissecting Lunes) - Numberphile

Neil Sloane is back, this time with some mathematical properties of Lunes. More links & stuff in full description below ↓↓↓ See more Neil Sloane videos on Numberphile: https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2 Neil is the founder of the On-Line Encyclopedia of Integer Sequences (OEIS): https://oeis.org/ Some OEIS sequences related to this video (to get you started)... https://oeis.org/A000217 https://oeis.org/A000124 Brady Haran videos relating to the Moon - https://www.youtube.com/playlist?list=PLXDUU63xAVsc Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Video by Brady Haran and Pete McPartlan Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

On-Line Encyclopedia of Integer Sequences

3 weeks ago·youtube.com

+30

Most people don’t see the trick of solving g this quintic equation

This quintic equation, (x-3)^5+(x-7)^5=(2x-10)^5 is purposely designed with a secret trick in mind! Do not expand it, but try a substitution instead! 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

(x-3)^5+(x-7)^5=(2x-10)^5

3 weeks ago·youtube.com

I discovered an AMAZING approximation of e (by accident)

I accidentally discovered an amazing approximation of e when I was teaching my summer calculus 1 class. If we cut a 10 meter rope into 2 pieces, one turns into an equilateral triangle, and the other turns into a square, what's the minimum combined area? This answer turns out to be really close to e! 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Mathematical constant e Area of geometric shapes

1 month ago·youtube.com

+31

The Mountain Climbing Theorem - Numberphile

Sophie Maclean discusses the Mountain Climbing Theorem. More links & stuff in full description below ↓↓↓ Sophie Playlist: https://www.youtube.com/playlist?list=PLt5AfwLFPxWJL8jqE19RlDCMJp7psCA6r Sophie Maclean is based at Kings College, London: https://sophiethemathmo.wordpress.com Brady's boiling water at Everest video - https://youtu.be/JTL4dj3Gx1o Some short clips from the Everest Base Camp Trek - https://www.youtube.com/playlist?list=PLky6yurD40o7BWCHu2kkQX8CZ5zrhxV2I Everest from a plane - https://www.youtube.com/watch?v=i3AK7c42mUY Grave of Everest - https://www.youtube.com/watch?v=hgYJOIrmSG0 The Everest Problem (Objectivity) - https://www.youtube.com/watch?v=gXBYWc4L83Q Letters from Everest (Objectivity) - https://www.youtube.com/watch?v=Y0cGW5bcQlM Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Video by Brady Haran & Pete McPartlan Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Mountain Climbing Theorem

1 month ago·youtube.com

+39

Forgetting the +C is not THAT BAD! (You won’t lose points on my tests, but…)

You should still put the +C after an indefinite integral! Get your +C t-shirt https://amzn.to/45h8v0A #calculus

Indefinite Integrals in Calculus

1 month ago·youtube.com

+12

They say 1-1+1-1+1-1+... is 1/2 (Grandi's Series fully explained)

Math tutorial answering the question from Reddit, why 1-1+1-1+1-1+... is 1/2? This is known as the Grandi's series. This question is from Reddit r/homeworkhelp https://www.reddit.com/r/HomeworkHelp/s/mG2OPxABKx Related links 1+2+3+...=-1/12 by@numberphile https://youtu.be/w-I6XTVZXww?si=9aEG3INL9delT4LI Cesàro Summation: https://en.wikipedia.org/wiki/Ces%C3%A0ro_summation Ramanujan Summation: https://en.wikipedia.org/wiki/Ramanujan_summation Cauchy Principal Value: https://en.wikipedia.org/wiki/Cauchy_principal_value 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Grandi's Series Cesàro Summation Ramanujan Summation

4 months ago·youtube.com

+15

f(5)=? American Invitational Mathematics Examination

We will solve a hard functional equation problem from the 2012 American Invitational Mathematics Examination (AIME) . Given f(0)=1, f(x)*f(2x^2)=f(2x^3+x), and f(2)+f(3)=125, we need to find f(5). This is a question asked by one of my viewers! 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

2012 American Invitational Mathematics Examination

4 months ago·youtube.com

A new "all-in-one" calculus problem (now in a matrix)

I crafted another all-in-one calculus problem, and this time I put the 4 main ingredients of calculus, i.e. limit, derivative, integral, and series, into a 2 by 2 matrix. Oh btw, we will also have to use the Lambert W function. #blackpenredpen #math

Calculus Problem Solving Lambert W Function

4 months ago·youtube.com

+30

Mathematician Attempts Art - Numberphile

Hannah Fry returns to Numberphile to showcase her art skills (and show us her new portrait at The Royal Society). See the Objectivity video (for more about the REAL artwork) at https://youtu.be/3HLxB5LbrDU More links & stuff in full description below ↓↓↓ (Real) artist Chloe Barnes can be found at: https://www.chloebarnesartist.com/ (and a handful of limited edition prints of her Hannah portrait were still available at the time we published this video!) Thanks also to artist Paulina Kwietniewska who did the painting of Chloe: https://paulinakwietniewska.com/ The Royal Society collections: https://royalsociety.org/about-us/what-we-do/collections/ Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Video by Brady Haran and James Hennessy Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Hannah Fry's Art at The Royal Society

4 months ago·youtube.com

+47

Proving the quadratic formula using calculus? (just my attempt)

I have been wondering if we could prove the quadratic formula using calculus, so here's what I came up with. It still involves mostly algebra but I will try to see if I can use Newton's method of doing so soon! 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Quadratic Formula Newton's Method

4 months ago·youtube.com

+18

4211 - The Party Pooper Prime - Numberphile

OEIS founder Neil Sloane on lines of primes, awkward primes... and a 'party pooper prime'. More of this interview at https://youtu.be/u-_8wX4cECo Jane Street's puzzle at https://jane-st.co/Numberphile-JS-NumberCross4 and more puzzles at https://jane-st.co/Numberphile-JS-Puzzles More links & stuff in full description below ↓↓↓ SOME RELEVANT OEIS SEQUENCES Lines of Primes: https://oeis.org/A373813 Awkward Primes: https://oeis.org/A393445 More videos with Neil Sloane: https://www.youtube.com/playlist?list=PLt5AfwLFPxWJXQqPe_llzWmTHMPb9QvV2 Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Videos by Brady Haran Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Thanks to ALL our eagle-eyed helpers at The Numberphile Society, especially today to Debbie, Josh and Steven

OEIS (Online Encyclopedia of Integer Sequences)Neil Sloane

4 months ago·youtube.com

+43

The Original Biggest Numbers - Numberphile

Richard Elwes discusses the original Big Numbers... long before the likes of Graham's Number and Tree(3). They are epic. More links & stuff in full description below ↓↓↓ More Richard on Numberphile: https://www.youtube.com/playlist?list=PLt5AfwLFPxWI42WXh1jnv51jHrcjatrk8 More big numbers on Numberphile: https://www.youtube.com/playlist?list=PLt5AfwLFPxWJ_FwchNAjB3xa8UnoKdmQI More about Richard Elwes (who is based at the University of Leeds): https://richardelwes.co.uk/ Richard's new book Huge Numbers Waterstones (UK): https://www.waterstones.com/book/huge-numbers/richard-elwes/9781399818827 Barnes and Noble (US): https://www.barnesandnoble.com/w/huge-numbers-richard-elwes/1147952914 Or Amazon (affiliate links)... UK: https://amzn.to/4bSZA8v US: https://amzn.to/4v3CIMp Here's the mega zoom of Patreon names: https://www.patreon.com/posts/154415033 Patreon: http://www.patreon.com/numberphile Numberphile is supported by Jane Street. Learn more about them (and exciting career opportunities) at: https://bit.ly/numberphile-janestreet We are also grateful for support from the Ben Delo Foundation - https://delo.org/ NUMBERPHILE Website: http://www.numberphile.com/ Video by Brady Haran and Pete McPartlan Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Tree(3)Graham's Number

5 months ago·youtube.com

+36

Can we have a right triangle with sides 1, x and x^2 (but the hypotenuse is x)

Just a quick, fun triangle question that I came up with a few days ago: Can we have a right triangle with sides 1, x, and x^2 BUT the hypotenuse is x? 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus

Pythagorean theorem

5 months ago·youtube.com

+20

Actions

Add Video